546. Remove Boxes
Remove Boxes (LeetCode 546) is a Hard Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Dynamic Programming (DP) Patterns pattern, in the Interval DP subpattern.
How to solve Remove Boxes
Remove Boxes is a Interval Dynamic Programming problem, part of Dynamic Programming (DP) Patterns. Solve problems on intervals like burst balloons and matrix chain multiplication using interval DP.
Work towards the solution in these steps:
- Think about using dynamic programming to optimize the removal process, as removing boxes in different orders affects the total points earned.
- Consider representing the problem as intervals of boxes and how removing certain continuous segments affects subsequent choices, which suggests interval DP.
- To capture the impact of previously removed boxes, try incorporating a parameter in your DP state that counts consecutive boxes of the same color adjacent to the current interval, enhancing your state representation.
The reference solution runs in O(n^3) time and O(n^3) space.
The Remove Boxes solution and editorial walks through the full approach with reference code.
Problem statement
You are given several boxes with different colors represented by different positive numbers.
You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of k boxes, k >= 1), remove them and get k k points.
Return the maximum points you can get.
Example 1:
Input: boxes = [1,3,2,2,2,3,4,3,1] Output: 23 Explanation: [1, 3, 2, 2, 2, 3, 4, 3, 1] ----> [1, 3, 3, 4, 3, 1] (33=9 points) ----> [1, 3, 3, 3, 1] (11=1 points) ----> [1, 1] (33=9 points) ----> [] (22=4 points)
Example 2:
Input: boxes = [1,1,1] Output: 9
Example 3:
Input: boxes = [1] Output: 1
Constraints:
- 1 <= boxes.length <= 100
- 1 <= boxes[i] <= 100
Topics and companies
Topics: Array, Dynamic Programming, Memoization.
Reported in interviews at Apple, Amazon.
How to practise Remove Boxes on Thita.ai
Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n^3) time and O(n^3) space.
Open Remove Boxes in the code editor, or read the Remove Boxes editorial for a worked solution with its approach and complexity analysis.
Where Remove Boxes sits in the DSA pattern sheet
Problems related to Remove Boxes
Other problems that use the same Interval DP and Dynamic Programming (DP) Patterns techniques:
- Burst Balloons — Hard, same subpattern
- Stone Game — Medium, same subpattern
- Stone Game II — Medium, same subpattern
- Best Time to Buy and Sell Stock — Easy, same pattern
- Best Time to Buy and Sell Stock II — Medium, same pattern
- Best Time to Buy and Sell Stock III — Hard, same pattern
Remove Boxes FAQ
What is the LeetCode number of Remove Boxes?
Remove Boxes is LeetCode problem 546, rated Hard.
What pattern is used to solve Remove Boxes?
Remove Boxes is a Interval Dynamic Programming problem. It belongs to the Dynamic Programming (DP) Patterns pattern, in the Interval DP subpattern.
What is the time complexity of Remove Boxes?
The reference solution runs in O(n^3) time and O(n^3) space.
Which companies ask Remove Boxes?
Remove Boxes has been reported in interviews at Apple, Amazon.